aâ‰8.6602, b=5, A=60 degrees
Let's calculate the lengths of the sides and angles and see what option fits.
Since the sum of the angles in a triangle equals 180 and we known 2 of the angles, let's calculate angle A first.
A = 180 - 90 - 30 = 60
Now for side b. This is a 30/60/90 triangle. The side opposite B is half the length of c since if you were to reflect the triangle across side a, you would have an equilateral triangle. So b is 10/2 = 5.
And finally, since we have a right triangle, we can use the Pythagorean theorem to get the remaining side a. So
a = sqrt(10^2 - 5^2) = sqrt(100 - 25) = sqrt(75) = 5*sqrt(3) ≠8.660254038
And of the available choices, only the last one matches which is
aâ‰8.6602, b=5, A=60 degrees
As a side note, the last option comes close, but isn't entirely correct since the properly rounded value for a should be 8.6603, not 8.6602.
